An improvement has been made on the construction method of Boolean Functions and the relevant conclusions of combinatorial conjecture proposed by Ziran Tu. We generalized their results and extended to the vectorial case. A class of bent Boolean functions F with the maximum algebraic immunity is presented by a more general construction method. Then by modifying F, we get new vectorial balanced functions with optimum algebraic degree, good nonlinearity and good algebraic immunity even maximum algebraic immunity for some cases.